1. Solving Exponentials By Graphing and Common Base

2. To Solve Exponential by Graphing Enter left side of equation into y 1 Enter right side of equation into y 2 Set window to see interesection 2 nd, trace, 5, enter, enter, enter Note: Inequalities work the same, except now you are looking to see if y 1 is greater/less than y 2

3. Example 1 2 x = 8 2 nd, trace, 5, enter, enter, enter y1y1 y2y2 X=3

4. Example 2 4 x+1 = 8 2x+3 2 nd, trace, 5, enter, enter, enter y1y1 y2y2 X=-1.75

5. Example 3 8 x+2 < 32 2 nd, trace, 5, enter, enter, enter y1y1 y2y2 X< -1/3

6. Example 4 2 3x+2 ≥ -2 2 nd, trace, 5, enter, enter, enter y1y1 y2y2 X ≥ -2

7. To Solve Exponential by Common Base Make sure that both sides of equal sign share a common base. Set the exponents equal to each other and solve.

8. Example 1 5 x = 5 3 -They both share a common base. -Set both exponents equal to each other and solve. x = 3 Base of 5

9. Example 2 10 1-x = 10 4 -They both share a common base. -Set both exponents equal to each other and solve. Base of 10 1-x = 4 -1 -1 -x = 3 x = 3

10. Example 3 7 6x = 7 2x-20 -They both share a common base. -Set both exponents equal to each other and solve. Base of 7 6x = 2x-20 -2x -2x 4x = -20 4 4 x = -5

11. Example 4 9 2x = 27 x-1 -They do NOT share a common base so we have to change the bases to be alike. -Set both exponents equal to each other and solve. Base of 9 Base of 27 (3 2 ) 2x = (3 3 ) x-1 2(2x) = 3(x-1) 4x = 3x – 3 -3x -3x x = -3 Base of 3

12. You Try Example 5 2 2x = 8 2x-4 -They do NOT share a common base so we have to change the bases to be alike. -then Set both exponents equal to each other and solve. Base of 2 Base of 8 (2) 2x = (2 3 ) 2x-4 2x = 3(2x-4) 2x = 6x-12 -6x -6x -4x = -12 -4 -4 x = 3 Base of 2

13. Example 6 9 x-4 = -They do NOT share a common base so we have to change the bases to be alike. -then Set both exponents equal to each other and solve. Base of 9 Base of 1/81 9 x-4 = (9 -2 ) x-4 = -2 +4 +4 x = 2 Base of 9

14. Example 7 81 3-x = -They do NOT share a common base so we have to change the bases to be alike. -then Set both exponents equal to each other and solve. Base of 81 Base of 1/3 (3 4 ) (3-x) = (3 -1 ) 5x-6 4(3-x) = -1(5x-6) 12-4x= -5x+6 12+x=6 x = -6 Base of 3

15. Example 8 25 10x+8 = 4-2x -They do NOT share a common base so we have to change the bases to be alike. -then Set both exponents equal to each other and solve. Base of 25 Base of 1/125 (5 2 ) 10x+8 =(5 -3 ) 4-2x 2(10x+8) = -3(4-2x) 20x+16 = -12+6x 14x+16 = -12 14x = -28 x = -2 Base of 5